Saturated ideals
Saturated ideals
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饱和的理想
DOI：
10.2307/2271949
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发表时间：
1978
影响因子：
0.6
通讯作者：
K. Kunen
中科院分区：
文献类型：
--
作者：
K. Kunen
本文给出了在不可达的κ上存在一个ω -饱和理想和在ω - 1上存在一个ω -饱和理想的一致性证明。我们还包括一项历史调查，概述了饱和理想的其他已知结果。§1。强迫。我们假定读者熟悉强制模型和布尔值模型的常用技术（参见Jech[3]或Rosser[11]），因此我们在这里只指定一些不太标准的符号。“cBa”是“完全布尔代数”的缩写。如果P （= [P, <›]）是一个强迫的概念，是相关的cBa。我们把VP写成。诸如κ闭合、κ完全等概念总是表示< κ。因此，如果每个长度小于κ的递减链都有下界，则P是κ-闭的；如果一个布尔代数的基数小于κ的子集总是存在，则P是κ-完备的。如果是cBa，那么在v中表示x时，x *是宾语。在许多情况下，特别是与序数连用时，省略了*。是表示V的布尔值类，即：
In this paper, we give consistency proofs for the existence of a κ-saturated ideal on an inaccessible κ, and for the existence of an ω2-saturated ideal on ω1. We also include an historical survey outlining other known results on saturated ideals. §1. Forcing. We assume that the reader is familiar with the usual techniques in forcing and Boolean-valued models (see Jech [3] or Rosser [11]), so we shall just specify here some of the less standard notation. “cBa” abbreviates “complete Boolean algebra”. If P (= ‹P, <›) is a notion of forcing, is the associated cBa. We write VP for . Notions like κ-closed, κ-complete, etc. always mean < κ. Thus, P is κ-closed iff every decreasing chain of length less than κ has a lower bound, and a Boolean algebra is κ-complete iff sups of subsets of of cardinality less than κ always exist. If is a cBa, x̌ is the object in representing x in V. In many cases, especially with ordinals, the ̌ is dropped. V̌ is the Boolean-valued class representing V — i.e.,